Q. 24 - An Introduction to General, Organic, and Biological Chemistry

Question

One of the components of gasoline is octane, ${\mathrm{C}}_8{\mathrm{H}}_{18}$, which has a density of $0.803 g/mL$. The combustion of $1$ mole of octane provides $5510 kJ$. A hybrid car has a fuel tank with a capacity of $11.9 gal$ and a gas mileage of $45 mi/gal$

1.   Write the balanced chemical equation for the combustion of octane. 
2.  Is the combustion of octane endothermic or exothermic? 
3.  How many moles of octane are in one tank of fuel, assuming it is all octane? 
4.  If the total mileage of this hybrid car for one year is $24500 mi$, how many kilograms of carbon dioxide would be produced from the combustion of the fuel, assuming it is all octane? 

Step-by-Step Solution

Answer

We get following as required answers:

1. $2 {\mathrm{C}}_8{\mathrm{H}}_{18}+ 25 {\mathrm{O}}_2\to 16 {\mathrm{CO}}_2+ 18{\mathrm{H}}_2\mathrm{O}+ \mathrm{Energy}$ is balanced equation for combustion of octane
2. Combustion of octane is exothermic in nature
3. $380.3 moles$ of octane can be in one tank of fuel.
4. $1670.720 kg$ carbon dioxide released in one year by hybrid car.

Part(a) Step 1: Given Information

We need to write balanced chemical equation of combustion of octane

Part(a) Step 2: Explanation

Molecular formula of octane= ${\mathrm{C}}_8{\mathrm{H}}_{18}$

Combustion means reaction of compound with oxygen. Below is balanced equation of combustion of octane:

$2 {\mathrm{C}}_8{\mathrm{H}}_{18}+25 {\mathrm{O}}_2\to 16 {\mathrm{CO}}_2 +18 {\mathrm{H}}_2\mathrm{O}+\mathrm{Energy}$

Part(b) Step 1: Given Information

 Specify whether combustion of octane endothermic or exothermic 

Part(b) Step 2: Explanation

As during combustion reaction energy is released in the form of  heat so energy is ejected in surrounding. So, combustion of octane is exothermic reaction. 

Part(c) Step 1: Given Information

We are given:

Capacity of fuel tank=$11.9 gal= 4546\times 11.9 mL= 54097 mL$

Density of octane=$0.803 g/mL$

 We need to find moles of octane assuming whole tank is filled with octane.

Part(c) Step 2: Explanation

Mass of octane in gallon= Volume*density

$=54097\times 0.803=43440.2$

Moles of octane present= $\frac{mass of oc\tan e present}{Molar mass of oc\tan e}=\frac{43440.2}{114.2}=380.3$

Hence, $380.3$ moles of octane will be present in fuel tank.

Part(d) Step 1: Given Information

We are given that mileage of car for one year is $24500 mi$ and gas has mileage of $45 mi/gal$

We need to find carbon dioxide released from combustion of fuel in whole year.

Part(d) Step 2: Explanation

If gas has mileage of $45 mi/gal$ than fuel consumed in one year=$\frac{24500 mil}{45 mil/gal}=5444.44 gal$

Mass of octane in $5444.44 gal$= $$\begin{gathered} 5444.44\times 4546\times 0.803 \\ =1987460.6 g \end{gathered}$$
(As mass = volume*density; $1 gal= 4546 mL$)

Moles of octane= $\frac{1987460.6}{114.2}=17403.3$

Two moles of octane on combustion gives $16$ moles carbon dioxide. So, one mole will give $8$ moles of carbon dioxide.

Total carbon dioxide moles released= $17403.3\times 8=139226.66$

Mass of carbon dioxide released= $\frac{139226.6\times 12}{1000}=1670.72 kg$